WorldCat Identities

Stillwell, John

Works: 73 works in 544 publications in 5 languages and 16,354 library holdings
Genres: History  Textbooks  Sources  Academic theses 
Roles: Author, Translator, Editor, htt, Illustrator, Author of introduction, tra
Publication Timeline
Most widely held works by John Stillwell
Mathematics and its history by John Stillwell( Book )

84 editions published between 1989 and 2020 in 5 languages and held by 2,528 WorldCat member libraries worldwide

Recoge los cambios en esta ciencia desde el teorema de Pitágoras hasta la computación, incluyendo breves biografías de matemáticos eminentes y ejercicios
Classical topology and combinatorial group theory by John Stillwell( Book )

38 editions published between 1980 and 2010 in English and German and held by 1,524 WorldCat member libraries worldwide

This is a well-balanced introduction to topology that stresses geometric aspects. Focusing on historical background and visual interpretation of results, it emphasizes spaces with few dimensions, where visualization is possible, and interaction with combinatorial group theory via the fundamental group. It also present algorithms for topological problems. Most of the results and proofs are known, but some have been simplified or placed in a new perspective. Over 300 illustrations, many interesting exercises, and challenging open problems are included. New in this edition is a chapter on unsolvable problems, which includes the first textbook proof that the main problem of topology, the homeomorphism problem, is unsolvable
Geometry of surfaces by John Stillwell( Book )

28 editions published between 1992 and 2010 in English and German and held by 1,275 WorldCat member libraries worldwide

"Geometry of Surfaces explores the interplay between geometry and topology in the simplest nontrivial case : the surfaces of constant curvature. As such, it provides a concise introduction to modern geometry for a wide audience. Requiring only a little prior knowledge of undergraduate mathematics, the book begins by discussing the three simplest surfaces : the Euclidean plane (zero curvature), the sphere (positive curvature), and the hyperbolic plane (negative curvature). Using the efficient machinery of isometry grouops, the author extends the discussion to all surfaces of constant curvature, which are typically obtained from the simplest ones by suitable isometries. The book then turns to the classification of the finitely many Euclidean and spherical surfaces and to a study of some remarkable hyperbolic surfaces. The general problem of classification is then considered from a topological and group-theoretic viewpoint. Because the theory of surfaces of constant curvature is intimately connected with the rest of modern mathematics, this book is an ideal starting point for students learning geometry, providing the simplest possible introduction to curvature, group actions, and covering spaces. The concepts developed here are, historically, the source of many concepts of complex analysis, differential geometry, topology, and combinatorial group theory, as well as such hot topics as fractal geometry and string theory. The prerequisites are modest, including only a little linear algebra, calculus, basic group theory, and basic topology. The formal coverage is extended by exercises and informal discussions throughout the text."--taken from back cover
Roads to infinity : the mathematics of truth and proof by John Stillwell( Book )

17 editions published in 2010 in English and held by 1,235 WorldCat member libraries worldwide

Offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics.--From publisher description
The four pillars of geometry by John Stillwell( Book )

26 editions published between 2005 and 2010 in English and held by 1,146 WorldCat member libraries worldwide

"The Four Pillars of Geometry approaches geometry in four different ways, devoting two chapters to each. This makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic. Not only does each approach offer a different view; the combination of viewpoints yields insights not available in most books at this level. For example, it is shown how algebra emerges from projective geometry, and how the hyperbolic plane emerges from the real projective line." "All readers are sure to find something new in this attractive text, which is abundantly supplemented with figures and exercises. This book will be useful for an undergraduate geometry course, a capstone course, or a course aimed at future high school teachers."--Jacket
Numbers and geometry by John Stillwell( Book )

17 editions published between 1997 and 1998 in English and German and held by 977 WorldCat member libraries worldwide

Numbers and Geometry is a beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis, and geometry - meet. The aim of this book is to give a broad view of these subjects at the level of calculus, without being a calculus (or a pre-calculus) book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. The key is algebra, which brings arithmetic and geometry together, and allows them to flourish and branch out in new directions
Sources of hyperbolic geometry by John Stillwell( )

17 editions published between 1996 and 1999 in English and held by 901 WorldCat member libraries worldwide

This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincaré that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue-not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincaré brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology. By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Poincaré in their full brilliance
Elements of algebra : geometry, numbers, equations by John Stillwell( Book )

32 editions published between 1994 and 2011 in 3 languages and held by 893 WorldCat member libraries worldwide

This book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory. Classical results in these fields, such as the straightedge-and-compass constructions and their relation to Fermat primes, are used to motivate and illustrate algebraic techniques. Classical algebra itself is used to motivate the problem of solvability by radicals and its solution via Galois theory. This historical approach has at least two advantages: On the one hand it shows that abstract concepts have concrete roots, and on the other it demonstrates the power of new concepts to solve old problems
Naive lie theory by John Stillwell( )

30 editions published between 2008 and 2012 in English and held by 804 WorldCat member libraries worldwide

Until recently, lie theory has been reserved for practictioners, with no lie theory for mathematical beginners. This book aims to fill that gap and it covers all the basics at a level appropriate for junior/senior level undergraduates
Reverse mathematics : proofs from the inside out by John Stillwell( )

19 editions published between 2018 and 2020 in English and held by 720 WorldCat member libraries worldwide

"This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics."--
Elements of mathematics : from Euclid to Gödel by John Stillwell( )

21 editions published between 2016 and 2018 in English and held by 717 WorldCat member libraries worldwide

"Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits."--Dust jacket
Elements of number theory by John Stillwell( Book )

27 editions published between 2002 and 2011 in 3 languages and held by 567 WorldCat member libraries worldwide

"This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. Finding integer solutions led to two fundamental ideas of number theory in ancient times - the Euclidean algorithm and unique prime factorization - and in modern times to two fundamental ideas of algebra - rings and ideals." "The development of these ideas, and the transition from ancient to modern, is the main theme of the book. The historical development has been followed where it helps to motivate the introduction of new concepts, but modern proofs have been used where they are simpler, more natural, or more interesting. These include some that have not yet appeared in textbooks, such as a treatment of the Pell equation using Conway's theory of quadratic forms. Also, this is the only elementary number theory book that includes significant applications of ideal theory. It is clearly written, well illustrated, and supplied with carefully designed exercises, making it a pleasure to use as an undergraduate textbook or for independent study."--Jacket
Yearning for the impossible : the surprising truths of mathematics by John Stillwell( Book )

16 editions published between 2006 and 2008 in English and held by 565 WorldCat member libraries worldwide

"This book explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress: - Irrational and Imaginary Numbers - The Fourth Dimension - Curved Space - Infinity and others The author puts these creations into a broader context involving related "impossibilities" from art, literature, philosophy, and physics. By imbedding mathematics into a broader cultural context and through his clever and enthusiastic explication of mathematical ideas the author broadens the horizon of students beyond the narrow confines of rote memorization and engages those who are curious about the place of mathematics in our intellectual landscape."--Page ublisher description
The real numbers : an introduction to set theory and analysis by John Stillwell( )

18 editions published in 2013 in English and held by 440 WorldCat member libraries worldwide

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory"uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis"the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor-Schröder-Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions
Ethnicity and integration by Maarten van Ham( )

1 edition published in 2010 in English and held by 344 WorldCat member libraries worldwide

The theme of this volume is ethnicity and the implications for integration of our increasingly ethnically diversified population. New research findings from a range of census, survey and administrative data sources are presented, and case studies are included
Lectures on number theory by Peter Gustav Lejeune Dirichlet( Book )

1 edition published in 1999 in English and held by 316 WorldCat member libraries worldwide

"This volume is a translation of Dirichlet's Vorlesungen uber Zahlentheorie which includes nine supplements by Dedekind and an introduction by John Stillwell, who translated the volume." "Lectures on Number Theory is the first of its kind on the subject matter. It covers most of the topics that are standard in a modern first course on number theory, but also includes Dirichlet's famous results on class numbers and primes in arithmetic progressions." "The book is suitable as a textbook, yet it also offers a fascinating historical perspective that links Gauss with modern number theory."--Jacket
Papers on Fuchsian functions by Henri Poincaré( Book )

10 editions published between 1985 and 2012 in English and German and held by 275 WorldCat member libraries worldwide

Mathematical evolutions( Book )

7 editions published in 2002 in English and held by 259 WorldCat member libraries worldwide

Yearning for the impossible : the surprising truths of mathematics by John Stillwell( )

8 editions published between 2006 and 2018 in English and held by 168 WorldCat member libraries worldwide

"This book explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress."--
A concise history of mathematics for philosophers by John Stillwell( )

8 editions published in 2019 in English and held by 155 WorldCat member libraries worldwide

This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics. -- Provided by publisher
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The four pillars of geometry
Classical topology and combinatorial group theoryGeometry of surfacesRoads to infinity : the mathematics of truth and proofThe four pillars of geometryNumbers and geometrySources of hyperbolic geometryElements of algebra : geometry, numbers, equationsNaive lie theory
Alternative Names
John Stillwell Australian mathematician

John Stillwell Australisch wiskundige

John Stillwell australischer Mathematiker

John Stillwell matamaiticeoir Astrálach

John Stillwell matemàtic australià

John Stillwell matemático australiano

John Stillwell matematikan australian

John Stillwell mathématicien australien

Stillwell, J.

Stillwell, J.C., 1942-

Stillwell, J. (John)

Stillwell, J.‏ (John), 1942-

Stillwell, John

Stillwell, John, 1942-

Stillwell, John C. 1942-

Stillwell, John C. (John Colin)

Stillwell, John Colin

Stillwell, John Colin 1942-

Джон Стиллвелл Австралийский математик

Джон Стілвелл

ג'ון סטילוול מתמטיקאי אוסטרלי

スティルウェル, J

スティルウェル, ジョン